Method of identifying geometric parameters of an articulated structure and of a set of reference frames of interest disposed on said structure

ABSTRACT

Parameters characterizing the orientation and the position of each sensor, including at least one accelerometer, are evaluated in the reference frame of each segment, together with the length of each segment, by using predetermined configurations and motions of a structure to which the sensors are attached. This makes it possible to provide a device for capturing the motions of a body with measurements which enables greater reliability of the measurements.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is the National Stage of International Application No.PCT/EP2013/054563, filed on Mar. 7, 2013, which claims the benefit ofFrench Application No. 1252101, filed Mar. 8, 2012. The contents of allof these applications are incorporated herein by reference.

BACKGROUND 1. Technical Field

Various embodiments relate to a method of identifying geometricparameters of an articulated structure and of an assembly of referenceframes of interest disposed on said structure, with the aid of atailored system of measurements.

The information evaluated can be the following:

-   -   The positions and orientations of the reference frames of        interest with respect to the structure;    -   The biomechanical parameters of the articulated structure (for        example the lengths of the segments).

Various embodiments of the invention are applicable, for example,without this list being limiting, to the following functions:

-   -   Accurately characterizing a system of measurements applied to        the articulated structure. The reference frames of interest are        then those of the measurement devices which instrument the        structure.    -   Measuring the kinetic parameters of a solid structure        (articulated or not). The reference frames of interest are        generally the points where one is interested in the kinetic        parameters.    -   Capturing the motion of an articulated body (sectors of        medicine, animation cinema, sport or else video games, research        in biomechanical analysis, in robotics, etc.).

2. Description of the Related Art

The fields of application in which articulated structures are used areexpanding. It is possible to cite, for example, robotics and human oranimal biomechanics. In these sectors, two types of information are ofimportance:

-   -   The geometry of the articulated structure; and    -   The position and the orientation of an assembly of reference        frames of interest (where for example temperature measurements,        kinetic measurements, etc. have been made available).

SUMMARY OF THE INVENTION

Various embodiments propose to treat these two problem areas jointlywithout resorting to the methods of the prior art, which principallyconsist in directly measuring the lengths of the segments of thearticulated structure (for example, with the aid of a tape measure orwith the aid of a complex optical system, etc.), in taking into accounta morphological model making it possible to simulate the dynamics ofsaid articulated structure and in locating the reference frames ofinterest on the segments also by direct measurement of their positionand orientation.

Various embodiment methods include associating a system of measurementsdistributed over said structure, said system comprising sensors fixedsecurely to the segment of said structure at the site of the points ofthe reference frames of interest so as to extract therefrom the desiredinformation described hereinabove.

Hereinafter in the document, we will illustrate embodiments of theinvention principally in an exemplary application in which:

-   -   The articulated structure is biomechanical and it is desired to        evaluate the length of its segments;    -   A motion measurements system is disposed on the articulated        structure and it is desired to identify their position and        orientation, the previously defined reference frames of interest        are those of each measurement element of the system; this system        serves at one and the same time for the measurement of the        motion and for the identification of the geometric parameters        making it possible to characterize the segments of the structure        and the position of reference frames of interest with respect to        them;    -   Said measurements system comprises at least one accelerometer.

For this purpose, various embodiment methods of determining the positionof an assembly of sensors in a reference frame tied to a segment of anarticulated chain are disclosed, in which the assembly of sensorscomprises at least one accelerometer and is secured to said articulatedchain, the method comprising: a first step of determining an orientationof a reference frame tied to the assembly of sensors with respect to thereference frame tied to said segment for at least one chosenconfiguration of said articulated chain; a second step of estimating amotion of said reference frame tied to the assembly of sensors in aterrestrial reference frame in the course of at least one motion of saidsegment; a third step of calculating said position of said assembly ofsensors in the reference frame tied to said segment, said third stepreceiving as input the estimation of the motion of said reference frametied to the sensor as output by the second step and the measurements ofsaid accelerometer in the course of said at least one motion.

Advantageously, the first step comprises a first sub-step of calculatinga first switching matrix for passing from said reference frame tied tothe assembly of sensors to a reference frame tied to the earth and asecond sub-step of calculating a second switching matrix for passingfrom said reference frame tied to the earth to a reference frame tied tosaid segment.

Advantageously, the first calculation sub-step uses at least onemeasurement of at least one second sensor of said assembly of sensors,said second sensor being able to provide measurements of at least onephysical field which is substantially uniform over time and in space orof rotation speed.

Advantageously, the first calculation step furthermore comprises acalculation sub-step prior to said first sub-step in the course of whicha third switching matrix for passing between a reference frame in motionand said reference frame tied to the earth is calculated, said thirdswitching matrix being either chosen or determined on the basis ofmeasurements of at least one physical field which is substantiallyuniform over time and in space or of the measurements of the rotationspeed of said reference frame in motion with respect to said referenceframe tied to the earth.

Advantageously, the first step is performed for at least twoconfigurations of said articulated chain.

Advantageously, prior to the first step, a first sub-step of determininga substantially invariant axis of rotation of said segment is carriedout.

Advantageously, the second step uses the outputs of at least one sensorchosen from the group comprising the accelerometer and a second sensorof said assembly of sensors, said second sensor being able to providemeasurements of at least one physical field which is substantiallyuniform over time and in space or of rotation speed.

Advantageously, in the course of the second step, said at least onemotion of the segment is a rotation around a substantially invariantaxis.

Advantageously, in the course of at least the second and third steps,use is made of a predictive model of the outputs of the accelerometerchosen as a function of the type of the motion of said segment and theposition is calculated of said assembly of sensors on said segment asoutput by an algorithm minimizing the errors between measured values andpredicted values.

Advantageously, said articulated chain comprises at least N segments, Nbeing greater than or equal to two.

Advantageously, a specific embodiment method further comprises a step inthe course of which the length of at least one segment of saidarticulated chain is calculated.

Advantageously, the calculation of a segment i inserted into anarticulated chain comprising j segments, j being greater than 1 and thani, is performed by solving the equationMat_tot_(mvt)*PosLong=Acc_(basis-free)(t_(initial)→t_(final)) in which:

-   -   Mat_tot_(mvt) is a matrix of dimension (i, j) whose coefficients        are calculated by

$\mspace{20mu}{{{{Mat}_{mvt}\left( {t,{{sensor}\mspace{14mu} j},{{sensor}\mspace{14mu} i}} \right)} = \left\lbrack {- \left( \frac{\partial_{1}^{{Sensori}_{{{Rotation}{(t)}}{Earth}}}}{\partial t^{2}} \right)_{\begin{matrix}{{reference}\mspace{11mu}{frame}} \\{{sensor}\mspace{14mu} j}\end{matrix}}} \right\rbrack},\mspace{20mu}{{PosLong} = \begin{bmatrix} \\{{Position}\mspace{14mu}{origin}_{{segment}\mspace{14mu} 2}} \\{Position}_{{sensor}\mspace{14mu} 2} \\\vdots \\{{Position}\mspace{14mu}{origin}_{{segment}\mspace{14mu} N}} \\{Position}_{{sensor}\mspace{14mu} N}\end{bmatrix}}}$   PosLong  is  the  vector

-   -   The basis-free acceleration at the instant t is calculated by        the formula

${{Acc}_{{basis} - {free}}(t)} = {{{Meas}_{Acc}(t)} - {G\; 0_{\begin{matrix}{{reference}\mspace{11mu}{frame}} \\{sensor}\end{matrix}}} + {Acc}_{{assembly}_{referenceframesensor}}}$

Advantageously, said articulated chain is a part of a human body or of ahumanoid structure.

Advantageously, the configurations of said articulated chain aredetermined by execution of at least N predefined successive gestures,each gesture enabling only a rotation of all or some of the segments ofsaid chain in a unique plane about a unique axis passing through anarticulation linking two segments, the segments other than the twostated segments remaining aligned during said rotation, in such a waythat rotations of segments are executed about at least N distinct axes.

Advantageously, N is greater than or equal to 3, a first segmentcorresponding to a shoulder, a second segment corresponding to an armlinked to the shoulder and a third segment corresponding to a forearmlinked to the arm by an elbow, the execution of predefined gesturesincluding, in this order: a rotation of the entire body about a verticalaxis (105) that may be regarded as the axis of the body, theshoulder-arm-forearm assembly being held outstretched in a horizontalplane during the rotation of the body about said axis, and; a rotationof the arm-forearm assembly about a horizontal axis (205) passingthrough the articulation linking the shoulder to the arm, thearm-forearm assembly being held outstretched during said rotation, and;a rotation of the forearm about a horizontal axis (305) passing throughthe elbow linking the arm to the forearm, the shoulder-arm assemblybeing held outstretched during said rotation.

Advantageously, each rotation of segments is executed about an axispassing through an articulation.

Various embodiments also disclose a system for determining the positionof an assembly of sensors in a reference frame tied to a segment of anarticulated chain, said assembly of sensors comprising at least oneaccelerometer and being secured to said articulated chain, said systemcomprising a first module for determining an orientation of a referenceframe tied to the assembly of sensors to said reference frame tied tosaid segment for at least one configuration of said articulated chain; asecond module for estimating a motion of said reference frame tied tothe assembly of sensors in a terrestrial reference frame in the courseof at least one motion of said segment; a third module for calculatingsaid position of said assembly of sensors in the reference frame tied tosaid segment, said third module receiving as input the estimation of themotion of said reference frame tied to the sensor as output by thesecond module and the measurements of said accelerometer in the courseof said at least one motion.

The principal advantage of certain embodiments is that of identifying,in an accurate, automatic, fast and practical manner, critical geometricparameters of an articulated structure and of a plurality of referenceframes of interest. In some of its embodiments, the invention isparticularly advantageous since it expresses the estimation of saidparameters in the form of a linear least squares problem, thecalculation of the estimate is therefore explicit and optimal.

BRIEF DESCRIPTION OF THE DRAWINGS

Other characteristics and advantages of the invention will becomeapparent with the aid of the description which follows offered withregard to the following figures which illustrate examples ofimplementation of the method according to certain non-limitingembodiments of the present invention:

FIG. 1 specifies the reference frames used in the description of thepresent invention;

FIG. 2 represents a general flowchart of the processing operations inseveral embodiments of the invention;

FIGS. 3a to 3e represent alternative variants of the invention inseveral of its embodiments;

FIG. 4 illustrates the articulated structure (human being in the figure)equipped with an assembly of devices and with the associated system ofmeasurements which will make it possible to identify the geometricparameters of the structure and devices whose reference frames are thereference frames of interest;

FIG. 5 illustrates a first motion of a human being wearing sensors of ameasurement system whose reference frames are the reference frames ofinterest, in an embodiment of the invention;

FIG. 6 illustrates a second motion of a human being wearing sensors of ameasurement system whose reference frames are the reference frames ofinterest, in an embodiment of the invention; and

FIG. 7 illustrates a third motion of a human being wearing sensors of ameasurement system whose reference frames are the reference frames ofinterest, in an embodiment of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

An articulated structure is composed of at least one first segment whichcan be mobile in space. The following segments are attached onefollowing the other in the form of a tree possibly comprising severalbranches.

The system of measurements comprises sensors, disposed on the segmentsof the articulated structure, whose reference frames are the referenceframes of interest.

Various embodiments are aimed at a method utilizing:

-   -   Means for measuring the orientation of the reference frames of        interest, sensors of the system of measurements or segments,    -   The sensors worn of the system of measurements comprising at        least one accelerometer,    -   Gestures to be performed;        so as to extract therefrom:    -   The position and the orientation of the reference frames of        interest on each segment,    -   If appropriate, the length of each segment.

FIG. 1 specifies the reference frames used in a description of specificembodiments.

R_(D) is the reference frame of interest, 101. The sensors making itpossible to perform the measurements will be placed on the referenceframe of interest, at least for the time of the measurement. In thesubsequent description, the expressions “reference frame of interest” or“reference frame tied to the assembly of sensors” will be usedalternatively to designate the reference 101.R_(S) is the reference frame tied to the segment, 102.R_(g) is the reference frame tied to the center of gravity of the body,103.R_(T) is the fixed reference frame, 104. The fixed reference frame isfor example tied to the Earth.

FIG. 2 represents a general flowchart of the processing operations inseveral embodiments of the invention.

This entails determining the parameters which characterize the positionand the orientation of the reference frames of interest with respect tothe segments which constitute the branches of the articulated structure.

Accordingly, it is desirable firstly to determine the orientation of thereference frame tied to the assembly of sensors (or reference frame ofinterest), 101 with respect to the reference frame of the segment 102.This orientation can be a directly accessible data item or it can bedetermined in one or more configurations of the articulated structure,as illustrated further on in the description.

The articulated structure is also made to perform at least one more orless simple motion, so as to obtain measurements of the parameters oforientation and of position of the reference frame tied to the assemblyof sensors employed, so as to solve the equation for the motions whichare performed and to deduce therefrom the estimation of the parameterswhich characterize the position of the assembly of sensors in thereference frame of the segment.

Thus, according to an embodiment of the invention, in the course of afirst step 201, 202, one may fix the orientation of the sensor assemblydirectly in the reference frame of the segment 103, or one may determinethe orientation of the assembly of sensors (for example the references401, 401 a, 402, 402 a, 403, 403 a of FIG. 4) in the reference frame thefixed reference frame, 104, by making the articulated structure take oneor more configurations, which make it possible to determine saidorientation, and therefore a switching matrix for passing between thereference frame 101 and the reference frame 104, and then a switchingmatrix for passing from the reference frame 104 to the reference frame102 is determined.

Thereafter, in an embodiment, in the course of a step 203, thearticulated structure is made to perform at least one motion for whichit is possible to determine a predictive model of the measurements ofthe sensors belonging to the assembly of sensors 401, 401 a, 402, 402 a,403, 403 a.

Alternative variants for carrying out steps 201 and 203 are illustratedin the subsequent description.

In FIG. 3a is represented the flowchart of the processing operations ofFIG. 2 in a first embodiment.

The assembly of sensors (references 401, 401 a, 402, 402 a, 403, 403 aof FIG. 4) comprises a means for measuring the orientation Mat_(RD) _(→)_(RT) of the reference frames of interest 101 with respect to the fixedreference frame tied to the Earth (R_(T), 104). Various sensors arecapable of providing measurements with respect to fields that aresubstantially invariant over time and in space (gravity, the terrestrialmagnetic field) or else with respect to a fixed reference in thereference frame 104, such as magnetic, optical, acoustic orradiofrequency sensors positioned in the assembly of sensors or on afixed base in conjunction with a fixed base with respect to thereference frame 104 or with sensors positioned in the assembly ofsensors. For example, gyrometers are capable of providing thisinformation. Magnetometers are also capable of playing this role, as areoptical, acoustic or radiofrequency means.

In this case, the first step 201, 202 which makes it possible toidentify the target matrix Mat_(RD) _(→) _(RS) includes adoptingpostures or poses that are predefined and therefore, known in the guiseof Mat_(RD) _(→) _(RT) and therefore, by transitivity of the rotationmatrices the matrix Mat_(RD) _(→) _(RS):Mat_(RD) _(→) _(RS)=Mat_(RD) _(→) _(RT)×(Mat_(RS) _(→) _(RT))⁻¹

The second step 203 includes performing gestures and in analyzing theaccelerometric measurement by utilizing the knowledge of Mat_(RD) _(→)_(RT) and Mat_(RD) _(→) _(RS) so as to estimate the parameters oflengths and distances, by applying the composition law for motions whichlinks the accelerations of the various points concerned.

The third step 204 of estimating the parameters for the position of theassembly of sensors on the segment is explained further on in thedescription.

Certain particular cases, illustrated by the flowchart of the processingoperations of FIG. 3b , suggest the addition of constraints on the typeof motions. For example, employing magnetometers as means for measuringthe orientations may constrain the gestures to comply with asubstantially invariant axis of rotation. A so-called “U constant”algorithm is then used to solve the equations for the motions asexplained further on in the description. Such an algorithm is disclosedin application EP1985233 belonging to the applicants of the presentapplication, which is incorporated herein by reference. Theconfigurations and motions which the articulated structure is to be madeto perform are illustrated in the embodiments described as commentary toFIGS. 5, 6 and 7.

FIG. 3c represents the flowchart of the processing operations of a2^(nd) embodiment in which a means is available for measuring theorientation Mat_(RD) _(→) _(R′), R′ being an arbitrary reference framewhose motion in the fixed reference frame R_(T) is known or that it ispossible to fix. This allows us to return to the previous case for steps203 and 204. For example, a system of directional antennas worn on theone hand at the level of the center of mass (R′), and on the other handat the level of the reference frames of interest, makes it possible tofollow the motions of the reference frame R′ with respect to thereference frame of the earth, 104.

FIG. 3d represents the flowchart of the processing operations of a3^(rd) embodiment in which the orientation of the reference frame 101 inthe reference frame 102 is already available, where a means of measuringsaid orientation is available. A matrix Mat_(RD) _(→) _(RS) is thendetermined which makes it possible to pass directly from the referenceframe of interest to the reference frame of the segment, therebycarrying out the first step 201, 202 of the method of the invention. Forexample, it is possible to use the means cited in patent applicationEP1985233 belonging to the applicants of the present application,already cited. These means may comprise just an accelerometer or, infact the same sensors as those of the system of measurements ofembodiments of the invention. According to various embodiments, at leasttwo substantially invariant axes of rotation of the segment instrumentedwith the sensor or sensors are determined. The rotation motions aredetermined as substantially invariant with respect to one or morethresholds chosen by the user of the system.

The second step 203 includes performing protocol motions, for which itis desirable to impose the trajectory of all the equipped segments(X,Y,Z) independently of time or of the execution speed profile. Theaccelerometric data item measured in the course of time during thisgesture is then compared elastically (elastic deformation of time) withthe expected measurement model tied to the predefined trajectory forexample by an error minimization operation or likelihood ratiomaximization operation whose variables are the parameters sought.

The third step 204 (which may, if appropriate, be simultaneous with step203) of estimating the parameters for the position of the assembly ofsensors on the segment is explained further on in the description.

FIG. 3e represents a flowchart of the processing operations of a 4^(th)embodiment of the invention in which a means is available for measuringthe orientation Mat_(RS) _(→) _(RT) of the segment in the fixedreference frame tied to the Earth, 103. The same means as those used inthe embodiment of FIG. 3a may be suitable, for example, optical systems,ultrasound systems or any other system which has a fixed base in thereference frame tied to the Earth.

The first step 201, 202 includes performing protocol motions, withsubstantially invariant axis of rotation, so that with the aid of ameasurement system comprising at least one accelerometer, it is possibleto identify the rotation matrix Mat_(RD) _(→) _(RT) and thus return tothe first case hereinabove.

The third step 204 of estimating the parameters for the position of theassembly of sensors on the segment is explained further on in thedescription.

FIG. 4 illustrates a particular case where the articulated structure(400) is a human being who is equipped on a part only of their body:left shoulder and arm. The shoulder as well as the arm and the forearmare equipped respectively with the devices (401 a, 402 b, 403 b) and, atthe same locations the sensors of said system of measurements (401, 402,403).

FIG. 5 illustrates a first motion of a human being wearing sensors (401,402, 403) of a measurement system, in an embodiment of the invention. Inthis embodiment, the assembly of devices represented in FIG. 4 and thesystem of measurements are merged and consist of sensors which associateaccelerometers and magnetometers (Embodiment illustrated in FIG. 3b ).

This exemplary implementation of the invention makes it possible tocalibrate an assembly of three sensors 401, 402 and 403 tied to threesegments, namely the shoulder of a person, to which the sensor 401 isattached, the arm of the person, to which the sensor 402 is attached,and finally the forearm of the person, to which the sensor 403 isattached. For the present exemplary embodiment of the invention, theapplicants have used sensors 401, 402 and 403 marketed by one of theapplicants under the commercial name MotionPod and which each combine athree-axis accelerometer with a three-axis magnetometer. Each of thesensors 401, 402 and 403 transmits its data via a radio link to a boxcommonly called a Motion Controller, this box being linked to a computerby a USB link. The box and the computer are not represented in thefigure. The data are utilizable on the computer by virtue of aprogramming interface marketed by the applicants under the commercialname Smart Motion Development Kit (SMDK). The SMDK programming interfacemakes it possible either to obtain raw and calibrated measurements of aMotionPod, or to obtain an estimation of the orientation of a MotionPod.

Hereinafter, the terms sensor, or MotionPod will be used interchangeablyto designate the elements 401, 402 and 403 represented in FIGS. 4, 5, 6and 7.

Prior to the use of the system thus including the sensors 401, 402 and403, for example to capture the motions of the assembly with threesegments shoulder-arm-forearm of the person, it is desirable to evaluatethe change of reference frame between the reference frame of the solidthat constitutes each segment and the reference frame of the sensorattached to said segment. Thus, it is desirable to evaluate the changeof reference frame between the reference frame of the shoulder and thesensor 401, the change of reference frame between the reference frame ofthe arm and the sensor 402, as well as the change of reference framebetween the reference frame of the forearm and the sensor 403. It isalso desirable to evaluate the changes of reference frame between thevarious segments. This is an object of the method of identifying thegeometric parameters according various embodiments of the invention. Inthe present exemplary embodiment, this entails firstly evaluating theorientation of each of the sensors 401, 402 and 403 with respect to thesegment to which said sensor is attached by using the means formeasuring the orientation and optionally protocol gestures (see thevarious embodiments described hereinabove as commentary to FIGS. 3a to3e ). Thereafter it entails evaluating the position of each of thesensors 401, 402 and 403 with respect to the segment to which saidsensor is attached in the form of a position vector. It also entailsevaluating the length of each of the three segments in the form of alength vector. It should be noted that the position of the sensors couldbe measured with a rule, but the estimation obtained may turn out to betoo coarse; furthermore, only the component, referenced X in FIGS. 5, 6and 7, along the length of each of the segments can actually beevaluated by this manual procedure.

The method of identifying the geometric parameters according to variousembodiments of the invention comprises a step of evaluating theorientation of the sensors. In this exemplary embodiment (FIGS. 5, 6,7), this entails notably giving the body a series of predefined staticpostures and comparing the actual measurements with theoretical values,so as to determine the orientation parameters. The larger the series,the better the accuracy. A single measurement is sufficient if themagnetic field is known perfectly and if the orientation of the segmentis determined exactly, but this is not the case in human motions.

Thus, for example, the body is firstly placed in a posture termed“posture 1” which corresponds to the reference posture, that is to saywith all the angles at 0. Next it is rotated (for example) 90°clockwise, to attain the posture termed “posture 2”. It is then knownthat the sensors 401, 402 and 403 measure (the equations being valid forall these sensors):

 = R_orientation * G 0 MeasureMagneto_(Positive 1) = R_orientation * H 0$\mspace{20mu}{{MeasureAccelero}_{{Posture}\mspace{11mu} 2} = {{R\_ orientation}*\begin{bmatrix}0 & {- 1} & 0 \\1 & 0 & 0 \\0 & 0 & 1\end{bmatrix}*G\; 0}}$$\mspace{20mu}{{MeasureMagneto}_{{Posture}\mspace{11mu} 2} = {{R\_ orientation}*\begin{bmatrix}0 & {- 1} & 0 \\1 & 0 & 0 \\0 & 0 & 1\end{bmatrix}*H\; 0}}$

Where:

-   -   MeasureAccelero_(Posture k) designates a measurement taken by        the accelerometer when the body occupies the posture k∈{1,2};    -   MeasureMagneto_(Posture k) designates a measurement taken by the        magnetometer when the body occupies the posture k∈{1,2};    -   {right arrow over (G)} a designates the terrestrial        gravitational field;    -   {right arrow over (H)} designates the terrestrial magnetic        field;    -   (GH) designates the angle between {right arrow over (G)} and        {right arrow over (H)};

${G\; 0} = \begin{bmatrix}0 \\0 \\1\end{bmatrix}$ and ${H\; 0} = \begin{bmatrix}{\sin({GH})} \\0 \\{\cos({GH})}\end{bmatrix}$respectively designate the values of the fields {right arrow over (G)}and {right arrow over (H)} in a given initial position and measured inthe reference frame of the sensor;

-   -   R_orientation designates the rotation matrix to be identified.

Indeed, by convention the Z axis is vertical and is oriented downwards.Several quantities may be determined: the orientation matrixR_orientation and the values of sin(GH) and cos(GH). Accordingly, thefollowing calculations can be performed:

⁢=   MeasureAccelero Posture ⁢ ⁢ 2 = MeasureAccelero Posture ⁢ ⁢ 2 MeasureAccelero Posture ⁢ ⁢ 2  =   MeasureMagneto Posture ⁢ ⁢ 2 =MeasureAccelero Posture ⁢ ⁢ 2  MeasureAccelero Posture ⁢ ⁢ 2 

This yields:sin(GH)=mean(∥MeasureAccelero_(Posture 1)×MeasureMagneto_(Posture 1)∥,∥MeasureAccelero_(Posture 1)×MeasureMagneto_(Posture 2)∥)cos(GH)=mean(MeasureAccelero_(Posture 1)□MeasureMagneto_(Posture 1),MeasureAccelero_(Posture 2)□MeasureMagneto_(Posture 2))

It is noted that the first expression (sin(GH)) is a mean of the vectorproducts of the measurements of the sensors used and that the secondexpression (cos(GH)) is a mean of the scalar products of themeasurements of the sensors used.

Finally, the rotation matrix R_orientation is determined by:

Mat = [MeasureAccelero_(Posture  1), MeasureMagneto_(Posture  1), MeasureMagneto_(Posture  2)]$\mspace{79mu}{{R\_ orientation} = {{Mat}*\begin{bmatrix}0 & {\sin({GH})} & 0 \\0 & 0 & {- {\sin({GH})}} \\1 & {\cos({GH})} & {\cos({GH})}\end{bmatrix}^{- 1}}}$

This data item is then included in the model of measurements of thesensors in triplet angle form.

To proceed with the identification of the geometric parameters in thisembodiment, a step is carried out of evaluating the lengths of thesegments and positions of the sensors on the segments by virtue of aprotocol of gestures. This step can rely on an algorithm aimed atreducing the number of degrees of freedom by enabling only planarrotations in relation to constant axes, doing thus so as to utilize thea priori knowledge of the constant vector to solve the system.

Initially, the method for detecting a substantially invariant axis ofrotation, described in patent EP1985233 already cited, makes itpossible, using solely the measurements of the magnetometers under theplanar motion condition to which the structure of the sensors isconstrained, to retrieve the motion, that is to say to deduce the axisof rotation in the reference frame of the magnetometer and of theaccelerometer, and also to deduce the angle of rotation. This makes itpossible to validate the evaluation of the orientation of the sensorsperformed at the previous step and even to refine it. This also makes itpossible to verify that the orientation of the various sensors is indeedthe same, that is to say that the axis of rotation calculated on thebasis of the measurements of the accelerometer is identical to thatcalculated on the basis of the measurements of the magnetometerundergoing the same planar motion. If such is not the case, it isdesirable to perform an identification of the box geometric parameters,that is to say an identification of the geometric parameters that relateto the relative orientation of the magnetometer and of theaccelerometer.

Subsequently, the measurements of the accelerometers are used todetermine the distance from each sensor to the axis of rotation. Themeasurements are transformed into the reference frame expected by virtueof the orientation matrices evaluated during the previous step, doingthus so as to work with respect to the segments of the body and not withrespect to the sensors. The identification of the geometric parametersare preferably done in the order in which they are described in thepresent exemplary embodiment. The axes of rotation naturally passthrough the articulations of the body. It is therefore desirable todefine a protocol to excite sufficient axes so as to determine the threecomponents of the length and position vectors.

FIG. 5 illustrates a rotation of the entire body about a vertical axis505 that may be regarded as the axis of the body, theshoulder-arm-forearm assembly being held outstretched in a horizontalplane during the rotation of the body about the axis A1. We define:

$\theta_{a} = {\underset{{i = 1},2,3}{mean}\left( {{Uconstant}\left( {Mag}_{i} \right)} \right)}$${\overset{.}{\theta}}_{a} = \frac{d\;\theta_{a}}{d\; t}$

Where:

-   -   Mag_(i) designates the measurement taken by the magnetometer of        the sensor i∈{1, 2, 3};    -   Uconstant designates a function which returns the axis of        rotation obtained by the method described in patent EP1985233        already cited;    -   mean designates a function which returns the arithmetic mean.

We then have, for i=1, 2, 3:MeasureAccelero_(X,i) ^(a) =R _(i)*{dot over (θ)}_(a) ²

Where:

$\quad\left\{ \begin{matrix}{R_{1} = {{distance}\left( {{{basis}\mspace{14mu}{shoulder}},{sensor}_{1}} \right)}_{X}} \\\begin{matrix}{R_{2} = {{distance}\left( {{{basis}\mspace{14mu}{shoulder}},{sensor}_{2}} \right)}_{X}} \\{= {{{length}\mspace{14mu}({shoulder})_{X}} + {{distance}\left( {{{basis}\mspace{14mu}{arm}},{sensor}_{2}} \right)}_{X}}}\end{matrix} \\\begin{matrix}{R_{3} = {{distance}\left( {{{basis}\mspace{14mu}{shoulder}},{sensor}_{3}} \right)}_{X}} \\{= {{{length}\mspace{14mu}({shoulder})_{X}} + {{length}\mspace{14mu}({arm})_{X}} + {{distance}\left( {{elbow},{sensor}_{3}} \right)}_{X}}}\end{matrix}\end{matrix} \right.$

FIG. 6 illustrates a rotation of the arm-forearm assembly about ahorizontal axis 605, perpendicular to the plane of the figure andpassing through the articulation linking the shoulder to the arm, thearm-forearm assembly being held outstretched during the rotation. Wedefine:

$\theta_{b} = {\underset{{i = 2},3}{mean}\left( {{Uconstant}\left( {Mag}_{i} \right)} \right)}$${\overset{.}{\theta}}_{b} = \frac{d\;\theta_{b}}{d\; t}$

We then have, for i=2, 3:MeasureAccelero_(X,i) ^(b) =R _(i)*{dot over (θ)}_(b) ² +G*sin(θ_(b))

With:

$\quad\left\{ \begin{matrix}{R_{2} = {{distance}\left( {{{basis}\mspace{14mu}{arm}},{sensor}_{2}} \right)}_{X}} \\\begin{matrix}{R_{3} = {{distance}\left( {{{basis}\mspace{14mu}{arm}},{sensor}_{3}} \right)}_{X}} \\{= {{{length}\mspace{14mu}({arm})_{X}} + {{distance}\left( {{elbow},{sensor}_{3}} \right)}_{X}}}\end{matrix}\end{matrix} \right.$

FIG. 7 illustrates a rotation of the forearm about a horizontal axis705, perpendicular to the plane of the figure and passing through thearticulation linking the arm to the forearm, that is to say the elbow,the shoulder-arm assembly being held outstretched during the rotation.We define:

$\theta_{c} = {\underset{i = 3}{mean}\left( {{Uconstant}\left( {Mag}_{i} \right)} \right)}$${\overset{.}{\theta}}_{c} = \frac{d\;\theta_{c}}{d\; t}$

We then have:MeasureAcrelero_(X3) R ₃*{dot over (θ)}_(c) ² +G*sin(θ_(c))With:R ₃=distance(elbow,sensor₃)_(X)

Using the relations hereinabove, the following equations can be deduced:

$\quad\left\{ \begin{matrix}{{Position}_{X,1} = {{{distance}\left( {{{basis}\mspace{14mu}{shoulder}},{sensor}_{i}} \right)}_{X} = \left( \frac{{MeasureAccelero}_{X,1}^{a}}{{\overset{.}{\theta}}_{a}^{2}} \right)}} \\{{Position}_{X,2} = {{{distance}\left( {{{basis}\mspace{14mu}{arm}},{sensor}_{2}} \right)}_{X} = \left( \frac{\begin{matrix}{{MeasureAccelero}_{X,1}^{b} -} \\{\sin\left( \theta_{b} \right)*G}\end{matrix}}{{\overset{.}{\theta}}_{b}^{2}} \right)}} \\{{Position}_{X,3} = {{{distance}\left( {{elbow},{sensor}_{3}} \right)}_{X} = \left( \frac{\begin{matrix}{{MeasureAccelero}_{X,1}^{e} -} \\{\sin\left( \theta_{c} \right)*G}\end{matrix}}{{\overset{.}{\theta}}_{c}^{2}} \right)}}\end{matrix} \right.$

Finally, the lengths of the segments can be estimated according to the Xcomponent:

$\quad\left\{ \begin{matrix}\begin{matrix}{{Length}_{X\; 3} = {{{Length}({shoulder})}_{X} = {{distance}\left( {{{basis}\mspace{14mu}{shoulder}},{{base}\mspace{14mu}{arm}}} \right)}_{X}}} \\{= \left( {\frac{{MeasureAccelero}_{X\; 2}^{a}}{{\overset{.}{\theta}}_{a}^{2}} - {Position}_{X,2}} \right)}\end{matrix} \\\begin{matrix}{{Length}_{X,2} = {{{length}({arm})}_{X} = {{distance}\left( {{{basis}\mspace{14mu}{arm}},{elbow}} \right)}_{X}}} \\{= \left( {\frac{{MeasureAccelro}_{X\; 3}^{a}}{{\overset{.}{\theta}}_{a}^{2}} - {Length}_{X\; 3} - {Position}_{X,3}} \right)} \\{= \left( {\frac{{MeasureAccelero}_{X\; 3}^{b}}{{\overset{.}{\theta}}_{b}^{2}} - {Position}_{X,3}} \right)}\end{matrix}\end{matrix} \right.$

For the second length, it is preferable to evaluate the mean of the twoequations hereinabove to improve the quality of the estimation.

The same may be undertaken on the other axes of the body, so as todefine the other components of the length and position vectors.

While remaining entirely within the framework of the present invention,it is also possible to make the articulated structure perform lessconstrained motions than those used in the embodiments of FIGS. 5, 6 and7. In these cases, it may not be possible to apply the simplifiedpredictive models, used in these embodiments, of the measurements. Itwill, however, be possible to apply the various steps of embodiments ofthe method, it being understood that the 3^(rd) step of the method forestimating the parameters may call upon a more complex predictive modelof the measurements, for example that described in the patentapplication filed on the same day as the present application by the sameapplicants having the same inventor and having as title “PROCEDED'IDENTIFICATION DES PARAMETRES GEOMETRIQUES D'UNE STRUCTURE ARTICULEEET D'UN ENSEMBLE DE REPERES D'INTERET DISPOSES SUR LADITE STRUCTURE”[METHOD OF IDENTIFYING THE GEOMETRIC PARAMETERS OF AN ARTICULATEDSTRUCTURE AND OF AN ASSEMBLY OF REFERENCE FRAMES OF INTEREST DISPOSED ONSAID STRUCTURE], the contents of which are incorporated herein byreference. According to various embodiments of the invention, use ismade of the measurements model represented by the following equation:

${Meas\_ Acc} = {{{}_{}^{}{}_{}^{}}*\left( {{G\; 0} - \left( {\frac{\partial^{2}{{}_{}^{}{}_{}^{}}}{\partial t^{2}} + {Acc\_ assembly}} \right)} \right)}$

Indeed, we have the accelerometric measurements meas_acc and therepresentation of the motion by virtue of step 2 of the presentinvention. We can therefore construct the vector Acc_(basis-free) byvirtue of the equality:

${{Acc}_{{basis}\text{-}{free}}(t)} = {{{Meas}_{Acc}(t)} - {G\; 0_{\underset{sensor}{{reference}\mspace{14mu}{frame}}}} + {Acc}_{\underset{sensor}{{assembly}\mspace{14mu}{reference}\mspace{14mu}{frame}}}}$

We can also construct the matrix Mat_tot_(mvt) by virtue of theequality:

${Mat\_ tot}_{mvt} = \begin{bmatrix}{{Mat}_{mvt}\left( {t_{initial},{{sensor}\mspace{14mu} 1},{{sensor}\mspace{14mu} 1}} \right)} & \ldots & {{Mat}_{mvt}\left( {t_{initial},{{sensor}\mspace{14mu} 1},{{sensor}\mspace{14mu} N}} \right)} \\\vdots & \ddots & \vdots \\{{Mat}_{mvt}\left( {t_{final},{{sensor}\mspace{14mu} 1},{{sensor}\mspace{14mu} 1}} \right)} & \ldots & {{Mat}_{mvt}\left( {t_{final},{{sensor}\mspace{14mu} N},{{sensor}\mspace{14mu} N}} \right)} \\{{Mat}_{mvt}\left( {t_{initial},{{sensor}\mspace{14mu} 2},{{sensor}\mspace{14mu} 1}} \right)} & \ldots & {{Mat}_{mvt}\left( {t_{initial},{{sensor}\mspace{14mu} 2},{{sensor}\mspace{14mu} N}} \right)} \\\vdots & \ddots & \vdots \\{{Mat}_{mvt}\left( {t_{final},{{sensor}\mspace{14mu} 2},{{sensor}\mspace{14mu} 1}} \right)} & \ldots & {{Mat}_{mvt}\left( {t_{final},{{sensor}\mspace{14mu} 2},{{sensor}\mspace{14mu} N}} \right)} \\\vdots & \; & \vdots \\{{Mat}_{mvt}\left( {t_{initial},{{sensor}\mspace{14mu} N},{{sensor}\mspace{14mu} 1}} \right)} & \ldots & {{Mat}_{mvt}\left( {t_{initial},{{sensor}\mspace{14mu} N},{{sensor}\mspace{14mu} N}} \right)} \\\vdots & \ddots & \vdots \\{{Mat}_{mvt}\left( {t_{final},{{sensor}\mspace{14mu} N},{{sensor}\mspace{14mu} 1}} \right)} & \ldots & {{Mat}_{mvt}\left( {t_{final},{{sensor}\mspace{14mu} N},{{sensor}\mspace{14mu} N}} \right)}\end{bmatrix}$

With if i is in the chain between the origin of the skeleton and thesegment j

${{Mat}_{mvt}\left( {t,{{sensor}\mspace{14mu} j},{{sensor}\mspace{14mu} i}} \right)} = \left\lbrack {- \left( \frac{\partial^{2^{{sensor}\mspace{14mu} 1}{{Rotation}{(t)}}}{Earth}}{\partial t^{2}} \right)_{\underset{sensor}{{reference}\mspace{14mu}{frame}\mspace{14mu} i}}} \right\rbrack$     And  otherwise$\mspace{79mu}{{{Mat}_{mvt}\left( {t,{{sensor}\mspace{14mu} j},{{sensor}\mspace{14mu} i}} \right)} = \begin{bmatrix}0 & 0 & 0 \\0 & 0 & 0 \\0 & 0 & 0\end{bmatrix}}$

Once this matrix has been constructed, it merely remains to solve thefollowing least squares problem:

Mat_tot_(mvt) * PosLong = Acc_(basis − free)(t_(initial)− > t_(final))With ${PosLong} = \begin{bmatrix}{Position}_{{sensor}\mspace{14mu} 1} \\{{Position}\mspace{14mu}{origin}_{{segment}\mspace{14mu} 2}} \\{Position}_{{sensor}\mspace{14mu} 2} \\\vdots \\{{Position}\mspace{14mu}{origin}_{{segment}\mspace{14mu} N}} \\{Position}_{{sensor}\mspace{14mu} N}\end{bmatrix}$

Once PosLong has been estimated, it merely remains to collect theparameters according to the provision given in the above equality.

This procedure is advantageous since it expresses the estimation in theform of a linear least squares problem, the calculation of the estimateis therefore explicit and optimal.

According to embodiments of the invention (patent application filed onthe same day as the present application by the same applicants havingthe same inventor and having as title “PROCEDE D'IDENTIFICATION DESPARAMETRES GEOMETRIQUES D'UNE STRUCTURE ARTICULEE ET D'UN ENSEMBLE DEREPERES D'INTERET DISPOSES SUR LADITE STRUCTURE” [METHOD OF IDENTIFYINGTHE GEOMETRIC PARAMETERS OF AN ARTICULATED STRUCTURE AND OF AN ASSEMBLYOF REFERENCE FRAMES OF INTEREST DISPOSED ON SAID STRUCTURE],incorporated herein by reference, the measurement model isadvantageously solved, even if only a reduced number of gyrometers areavailable to supplement the accelerometer and magnetometer measurements,by calculating pseudo-static states which can be substituted, each timethat the system is in a pseudo-static state, for the values calculatedby a Kalman type state observer.

These steps of the method of various embodiments of the invention can beimplemented in software, certain parts of the software possibly beinginstalled onboard the sensors, others possibly being embedded in amicro-controller, a micro-processor, or a micro-computer connected tothe system of sensors. These processing capabilities can be conventionalcircuits, connected and configured to perform the processing operationsdescribed hereinabove.

The examples described hereinabove are given by way of illustration ofembodiments of the invention. They do not in any way limit the field ofthe invention, which is defined by the claims which follow.

The invention claimed is:
 1. A method of determining a position of anassembly of sensors in a segment reference frame associated with asegment of an articulated structure for use in capturing a motion of abody, the assembly of sensors comprising at least one accelerometer andbeing connected to the articulated structure, the method comprising:determining, based on measurements received from the accelerometer andat least one predetermined configuration of the articulated structure,an orientation of a sensor reference frame associated with the assemblyof sensors with respect to the segment reference frame, wherein thedetermining the orientation comprises calculating a first rotationmatrix for passing from the sensor reference frame to an earth referenceframe and calculating a second rotation matrix for passing from theearth reference frame to the segment reference frame, whereincalculating the first rotation matrix uses at least one measurement ofat least one second sensor of the assembly of sensors, the second sensorconfigured to provide measurements of at least one physical field whichis substantially uniform over time and in space or measurements ofrotation speed; estimating, based on the determined orientation, apredetermined motion of the sensor reference frame in the earthreference frame during at least one motion of the segment of thearticulated structure; calculating, based on the estimated predeterminedmotion, the position of the assembly of sensors in the segment referenceframe; and outputting, based on the calculated position, captured motionof the body.
 2. The method of claim 1, wherein prior to calculating thefirst rotation matrix a third rotation matrix is calculated for passingbetween a motion reference frame that is in motion and the earthreference frame, the third rotation matrix being calculated on a basisof the measurements of the at least one physical field which issubstantially uniform over time and in space or of the measurements ofthe rotational speed of the motion reference frame with respect to theearth reference frame.
 3. The method of claim 1, wherein eachcalculation is performed for at least two configurations of thearticulated structure.
 4. The method of claim 1, wherein, the motion ofthe sensor reference frame comprises a motion with a substantiallyinvariant axis of rotation.
 5. The method as claimed in claim 1, whereinestimating the predetermined motion uses the outputs of at least onesensor chosen from the group comprising the at least one accelerometerand the second sensor.
 6. The method as claimed in claim 1, wherein, inthe course of estimating the predetermined motion, said at least onemotion of the segment is a rotation around a substantially invariantaxis.
 7. The method as claimed in claim 1, wherein, in the course of atleast estimating the predetermined motion and calculating the position,use is made of a predictive model of the outputs of the at least oneaccelerometer chosen as a function of the type of the motion of saidsegment and the position is calculated of said assembly of sensors onsaid segment as output by an algorithm minimizing errors betweenmeasured values and predicted values.
 8. The method as claimed in claim1, wherein said articulated structure comprises at least N segments, Nbeing greater than or equal to two.
 9. The method as claimed in claim 8,further comprising: calculating the length of at least one segment ofsaid articulated structure.
 10. The method as claimed in claim 9,wherein calculation of a segment i inserted into the articulatedstructure comprising j segments, j being greater than 1 and greater thani, is performed by solving the equationMat_tot_(mvt)*PosLong=Acc_(basis-free)(t _(initial) →t _(final)) inwhich: Mat_tot_(mvt) is a matrix of dimension (i, j) whose coefficientsare calculated by the formula${{{Mat}_{mvt}\left( {i,{{sensor}\mspace{14mu} j},{{sensor}\mspace{14mu} i}} \right)} = \left\lbrack {- \left( \frac{\partial_{2}^{{Sensori}_{{{Rotation}{(t)}}_{Earth}}}}{\partial t^{2}} \right)_{\underset{{sensor}\mspace{14mu} j}{{reference}\mspace{14mu}{frame}}}} \right\rbrack},\mspace{79mu}{{PosLong} = {\begin{bmatrix}{Position}_{{sensor}\; 1} \\{{Position}\mspace{14mu}{origin}_{{segment}\mspace{14mu} 2}} \\{Position}_{{sensor}\mspace{14mu} 2} \\\vdots \\{{Position}\mspace{14mu}{origin}_{{segment}\mspace{14mu} N}} \\{Position}_{sensorN}\end{bmatrix}\mspace{79mu}{PosLong}\mspace{14mu}{is}\mspace{14mu}{the}\mspace{14mu}{vector}}}$The basis-free acceleration at the instant t is calculated by theformula${{Acc}_{{basis}\text{-}{free}}(t)} = {{{Meas}_{Acc}(t)} - {G\; 0_{\underset{sensor}{referenceframe}}} + {{Acc}_{{asssembly}_{referenceframesensor}}.}}$11. The method as claimed in claim 9, wherein said articulated structureis a part of a human body or of a humanoid structure.
 12. The method asclaimed in claim 11, wherein the at least one predeterminedconfiguration of said articulated structure is determined by executionof at least N predefined successive gestures, each gesture enabling onlya rotation of all or some of the segments of said structure in a uniqueplane about a unique axis passing through an articulation linking twosegments, the segments other than the two stated segments remainingaligned during said rotation, in such a way that rotations of segmentsare executed about at least N distinct axes.
 13. The method as claimedin claim 12, wherein N>=3, a first segment corresponding to a shoulder,a second segment corresponding to an arm linked to the shoulder and athird segment corresponding to a forearm linked to the arm by an elbow,the execution of predefined gestures including, in order: a rotation ofthe entire body about a vertical axis, the shoulder-arm-forearm assemblybeing held outstretched in a horizontal plane during the rotation of thebody about said axis, and; a rotation of the arm-forearm assembly abouta horizontal axis passing through the articulation linking the shoulderto the arm, the arm-forearm assembly being held outstretched during saidrotation, and; a rotation of the forearm about a horizontal axis passingthrough the elbow linking the arm to the forearm, the shoulder-armassembly being held outstretched during said rotation.
 14. The method asclaimed in claim 13, wherein each rotation of segments is executed aboutan axis passing through an articulation.
 15. A system for determining aposition of an assembly of sensors in a segment reference frameassociated with a segment of an articulated structure for use incapturing a motion of a body, the assembly of sensors comprising atleast one accelerometer and being connected to the articulatedstructure, the system comprising: a first module for determining, basedon measurements received from the accelerometer and at least onepredetermined configuration of the articulated structure, an orientationof a sensor reference frame associated with the assembly of sensors withrespect to the segment reference frame, wherein the determining theorientation comprises calculating a first rotation matrix for passingfrom the sensor reference frame to an earth reference frame andcalculating a second rotation matrix for passing from the earthreference frame to the segment reference frame, wherein calculating thefirst rotation matrix uses at least one measurement of at least onesecond sensor of the assembly of sensors, the second sensor configuredto provide measurements of at least one physical field which issubstantially uniform over time and in space or measurements of rotationspeed; a second module for estimating, based on the determinedorientation, a predetermined motion of the sensor reference frame in theearth reference frame during at least one motion of the segment of thearticulated structure; a third module for calculating, based on theestimated predetermined motion, the position of the assembly of sensorsin the segment reference frame; and a fourth module for outputting,based on the calculated position, captured motion of the body.